A base-10 integer n can be represented as $32_a$ in one base and $13_b$ in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?
+2666 We have: \(3a + 2 = b + 3\)
Rearrange as: \(3a = b + 1\)
We want a to be as small as possible, so \(a = 4\), meaning \(b = 11\)
This means that the sum is \(4 + 11 = \color{brown}\boxed{15}\)
